lyner

"Light travels in straight lines" is a statement which actually begs a very big question. It sort of assumes 'rays', which is not really the modern view of electromagnetic propagation. You can work out where images form or are seen by assuming that rays move through space (or a transparent medium). But a ray is supposed to be an infinitely thin beam of light (or a group of them), traveling in a single direction and you need an infinite aperture to form a beam like that, so it's hard to justify 'rays' in any other context than geometric optics, for designing lenses and the like. (It works very well and I'm not knocking it but it doesn't help basic understanding of what is going on.)Fermat's Principle says that light takes the shortest path (in terms of time taken) from one point to any other. That is a straight line in empty space but a curved one where gravity is significant or where the medium is not uniform.This is a question which is much easier to discuss in terms of waves, rather than particles.Huygens, yonks and yonks ago, introduced the idea of secondary wavelets when deciding where a wave was going to end up and in what direction the energy goes. It is the forerunner of diffraction theory, which takes a wave and determines how it will progress by integration over the whole of the space through it is traveling.

For propagation in a medium, you can treat the absorbing / re-radiating charge systems in much the same way as the Huygens secondary wave sources. (Remember, it isn't 'the electrons' that do the absorbing and radiating - it is the electrons plus the charges around them that determine the interction of the medium with the wave passing through the medium). The quantum nature (rather than the particle nature) of the propagated energy comes into the fact that individual atoms are involved. The radiation from each atom will be omnidirectional unless there is some regular structure (ref. syphrum's comment) - of which a WAVE treatment of the problem will produce a directional pattern into the probability distribution of the resulting direction of the energy. Basically, what I am saying is that it gets far too 'lumpy' to try to analyse what goes on in any detail by considering photons. Yes, they are absorbed and, yes there is a delay but I contend that you are onto a loser if you want to explain it in terms of little bullets traveling through the medium and bashing into electrons. If you don't treat the problem as one involving waves then even Snell's Law (which we all know and love from School) is more or less impossible to derive.This may be unsatisfactory but we are supposed to be sophisticated enough to cope with duality SO be pragmatic and use the bit of the dual model which fits the problem.

Lets assume a light beam travels in glass. My pet theory says that time in glass and time in air is not the same. Time travels slower in glass than in air as their densities are different. Thus the light emerges at a different point than it is supposed to be. Thus Snell's law comes into play. I am trying to put some maths into this.

It is probably best to think even more generally about the way light travels in a variable density transparent medium. The photons of light are considerably "bigger" than the spacing between the atoms. (so this is not true for x rays which are smaller and subject to diffraction) The electromagnetic fields can therefore can interact with several atoms at the same time and disturb them slightly without creating any quantum interactions(this is why the material is transparent) causing a slight delay. The individual interactions are far too complicated ever to analyse but the overall effect is simple. The path of a beam of light sent through the medium between two points travels along the path that is quickest betwen these two points. If there are two alternative routes that take exactly the same (shortest)time the beam will split and pass along both of them. In the case of propagation in a uniform medium the shortest distance between two points is of course a straight line.

This simple relationship describes how all optical systems and lenses work.

When light enters a medium, it slows down. I have heard that this is because it is constantly exiting electrons in the medium and subsequently being re-emitted by those electrons a short time later.

Why does it then travel in a straight path?

I thought that electrons emit photons in a totally random direction, which would disperse a beam quite quickly.

No, the electrons or the charges in the solid, transparent medium, don't emit photons in a random direction; that would happen with "scattering" for example when you make a laser beam go through a gas or through air with smoke (infact this is the reason you can see the laser beam crossing the air).

The electronic absorption/re-emission of light depends on the direction of the wave's propagation too.

Anyway, the absorption/re-emission in a solid medium as glass is just a simplistic way of considering things, because, actually, is wrong. Have a look to this (from Physics Forums):

Quote

Do Photons Move Slower in a Solid Medium?

Contributed by ZapperZ. Edited and corrected by Gokul43201 and inha

This question appears often because it has been shown that in a normal, dispersive solid such as glass, the speed of light is slower than it is in vacuum. This FAQ will strictly deal with that scenario only and will not address light transport in anomalous medium, atomic vapor, metals, etc., and will only consider light within the visible range.

The process of describing light transport via the quantum mechanical description isn't trivial. The use of photons to explain such process involves the understanding of not just the properties of photons, but also the quantum mechanical properties of the material itself (something one learns in Solid State Physics). So this explanation will attempt to only provide a very general and rough idea of the process.

A common explanation that has been provided is that a photon moving through the material still moves at the speed of c, but when it encounters the atom of the material, it is absorbed by the atom via an atomic transition. After a very slight delay, a photon is then re-emitted. This explanation is incorrect and inconsistent with empirical observations. If this is what actually occurs, then the absorption spectrum will be discrete because atoms have only discrete energy states. Yet, in glass for example, we see almost the whole visible spectrum being transmitted with no discrete disruption in the measured speed. In fact, the index of refraction (which reflects the speed of light through that medium) varies continuously, rather than abruptly, with the frequency of light.

Secondly, if that assertion is true, then the index of refraction would ONLY depend on the type of atom in the material, and nothing else, since the atom is responsible for the absorption of the photon. Again, if this is true, then we see a problem when we apply this to carbon, let's say. The index of refraction of graphite and diamond are different from each other. Yet, both are made up of carbon atoms. In fact, if we look at graphite alone, the index of refraction is different along different crystal directions. Obviously, materials with identical atoms can have different index of refraction. So it points to the evidence that it may have nothing to do with an "atomic transition".

When atoms and molecules form a solid, they start to lose most of their individual identity and form a "collective behavior" with other atoms. It is as the result of this collective behavior that one obtains a metal, insulator, semiconductor, etc. Almost all of the properties of solids that we are familiar with are the results of the collective properties of the solid as a whole, not the properties of the individual atoms. The same applies to how a photon moves through a solid.

A solid has a network of ions and electrons fixed in a "lattice". Think of this as a network of balls connected to each other by springs. Because of this, they have what is known as "collective vibrational modes", often called phonons. These are quanta of lattice vibrations, similar to photons being the quanta of EM radiation. It is these vibrational modes that can absorb a photon. So when a photon encounters a solid, and it can interact with an available phonon mode (i.e. something similar to a resonance condition), this photon can be absorbed by the solid and then converted to heat (it is the energy of these vibrations or phonons that we commonly refer to as heat). The solid is then opaque to this particular photon (i.e. at that frequency). Now, unlike the atomic orbitals, the phonon spectrum can be broad and continuous over a large frequency range. That is why all materials have a "bandwidth" of transmission or absorption. The width here depends on how wide the phonon spectrum is.

On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. This is similar to trying to oscillate something at a different frequency than the resonance frequency. So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its way through the material and this accumulate the delay.

Moral of the story: the properties of a solid that we are familiar with have more to do with the "collective" behavior of a large number of atoms interacting with each other. In most cases, these do not reflect the properties of the individual, isolated atoms.

« Last Edit: 18/08/2009 12:54:48 by lightarrow »

Logged

lyner

There's too much in that quote to deal with at once but there is a serious error when he states that atomic transitions in a solid correspond to discrete frequencies. In the solid state, the energies occur in bands, so the material will interact with a continuous spectrum and not with lines. Glass does have dispersion and absorption at higher frequencies than light, presumably because of the band structure.

Even if the energy re radiated from each atom is omnidirectional, the sum of all re radiated photons will just be a delayed version of the incident energy. The Huygens argument says that the resultant wave will be in the direction of the incIdent wave. I don't think the situation is the same as scattering in a gas because the scattering centres are smaller and closer together.

Having looked at the reference, it seems thet the particle approach is just harder. It seems to be just standing up in a hammock for the sake of it. (lightarrow you may need to search for that reference. I'll be interested if you 'get it')

The way that a solid behaves 'as a bulk' seems to be the way to deal with it.

There's too much in that quote to deal with at once but there is a serious error when he states that atomic transitions in a solid correspond to discrete frequencies. In the solid state, the energies occur in bands, so the material will interact with a continuous spectrum and not with lines.

Isn't this a confirmation of the fact that you can't treat atoms as they were independent?

Quote

Glass does have dispersion and absorption at higher frequencies than light, presumably because of the band structure.

Even if the energy re radiated from each atom is omnidirectional, the sum of all re radiated photons will just be a delayed version of the incident energy. The Huygens argument says that the resultant wave will be in the direction of the incIdent wave.

But there would be some waves propagating in all directions. Scattering is a completely different situation.

Quote

I don't think the situation is the same as scattering in a gas because the scattering centres are smaller and closer together.

Having looked at the reference, it seems thet the particle approach is just harder. It seems to be just standing up in a hammock for the sake of it. (lightarrow you may need to search for that reference. I'll be interested if you 'get it')

The way that a solid behaves 'as a bulk' seems to be the way to deal with it.

lyner

Yes - you are right - you can't treat atoms as if they are independent. Little bullets hitting them is too naive a model. However, if you really want photons to exist all the time and they are localised in some way, then they would interact with a localised bit of the medium and re-radiate. This would mean that the atoms would not have discrete energy levels, because of the presence of all their neighbours.The sum of all these events would not necessarily involve spreading the beam any more than a loaded transmission line, with lumped components, need not produce a reflected wave. The phases of each of the re-radiated bits of energy (Photons, perhaps) will / may be constructive in only one direction if the aperture is large enough. Classical diffraction theory tells you that your (finite width) lens / prism / glass block will always produce an amount of spreading.

Even a simple thing like a Yagi antenna will produce zero energy in the backward direction if designed correctly. The elements are all (but the driven one) 'lossless' , omndirectional absorbers / radiators. I don't think the coherence / non-coherence counts as long as the whole system, is considered.You are right that the scattering situation is different - I guess, because the scattering centres are independent of each other. That will be because they are very much less densely packed. How is it that you can treat isolated atoms / molecules as such broad band scatterers, I wonder, when they have characteristic absorption lines? I can understand that dust particles would be broadband but . . . molecules?

How is it that you can treat isolated atoms / molecules as such broad band scatterers, I wonder, when they have characteristic absorption lines? I can understand that dust particles would be broadband but . . . molecules?

Because in scattering (or at least in some specific kinds of it, as Rayleigh') there is no absorption/re-emission; the atom/molecule behaves as an electronic resonator, something as electrons in a metal, which reflects away every frequency.

Logged

lyner

But why should it do that? How can there be any interaction (gaining or losing energy) that doesn't fit the QM model of a molecule? At first sight, you seem to have to ignore the discrete energy levels of the atomic system - and that can't be right.Electrons in a metal only do what they do because of the band structure due to the vast number of nearby atoms and the Pauli thing. Where is the equivalent effect for an isolated gas molecule? Does the whole atom / molecule 'vibrate' in space because of a non-zero effective charge? I could imagine that would have a non discrete set of energy levels which could explain things. What does make sense to me is the possibility of Raleigh - type scattering for small conducting objects (particles of metal, perhaps).

But why should it do that? How can there be any interaction (gaining or losing energy) that doesn't fit the QM model of a molecule? At first sight, you seem to have to ignore the discrete energy levels of the atomic system - and that can't be right.

I was afraid of this question .In a simplistic sense I think we can say that, at least for single atoms/molecules, we can ignore the discrete energy levels when we don't have em frequencies corresponding to those levels' transition. Rayleigh's theory of scattering can be derived classically infact.

Quote

Electrons in a metal only do what they do because of the band structure due to the vast number of nearby atoms and the Pauli thing.

In this case I don't know what to say, probably it's not possible to reason simplistically and a full QED treatment is required. What I wonder however is: to absorb and then re-emit a visible photon, for example, one of such electrons should bring itself to an higher level and then 'fall' down again but this process requires time, even if very little (it's ≈ 10-8 s for common atomic transitions); does metallic reflection really has this (little) delay?

Quote

Where is the equivalent effect for an isolated gas molecule? Does the whole atom / molecule 'vibrate' in space because of a non-zero effective charge? I could imagine that would have a non discrete set of energy levels which could explain things. What does make sense to me is the possibility of Raleigh - type scattering for small conducting objects (particles of metal, perhaps).

A single atom/ molecule has a polarizability, so an em radiation generates periodic charges displacements in it, which in turn generate the scattered field.

I know it's slightly off topic, but in your original post you say "light travels in a straight line". Considering that light is affected (pulled off course) by gravity, and whereever you are in the universe, there's some form of gravity acting on you (all be it a very very small effect when you are not close to a large body), I wonder if light ever truly travels in a perfectly straight line?

Anyway, it wouldn't travel in a perfectly straight line even if there weren't any gravity, because light is subject to the phenomenon of 'diffraction': take a point-like source of light and put a coin in front of it, at some distance, and project the light in a screen behind the coin. If light would propagate in a perfectly straight line, you shouldn't have any light in the screen, exactly behind the coin; instead you have. Light 'goes behind the corners' of the coin.Light doesn't have 'nadelstrahlung' (needle-like emission).

If you believe Richard Feynman, because photons have no mass, they can travel at the speed of light. Because time slows down the faster you go, the photons that make up light never age, therefore, theoretically, they can be everywhere in the universe at any one time. Now, according to Feynman, light takes all possible paths to reach a particular destination. When added up as vectors, the sum of all of those paths gives the direction that the light we see has travelled. For simpler purposes, this is 'always' the shortest distance between the light source and where it is seen, and the photons themselves always travel in straight lines in every direction.

If you believe Richard Feynman, because photons have no mass, they can travel at the speed of light. Because time slows down the faster you go, the photons that make up light never age, therefore, theoretically, they can be everywhere in the universe at any one time. Now, according to Feynman, light takes all possible paths to reach a particular destination. When added up as vectors, the sum of all of those paths gives the direction that the light we see has travelled. For simpler purposes, this is 'always' the shortest distance between the light source and where it is seen, and the photons themselves always travel in straight lines in every direction.

So, you are saying that light never diffracts, never makes interference, never refracts? Explain, please.

This is where the whole particle/wave problem comes into play. I can't fully explain, but interference, diffraction and refraction are all properties occuring due to the wave characteristic of light, while my explanation was referring to the particle model and I can't explain how the particle/wave theories are linked.

This is where the whole particle/wave problem comes into play. I can't fully explain, but interference, diffraction and refraction are all properties occuring due to the wave characteristic of light, while my explanation was referring to the particle model and I can't explain how the particle/wave theories are linked.

They are linked in a simple way: you talk about waves between source and detector, that is, in absence of any interaction; you talk about photons in the detectors, that is, when there is interaction.

Most of us probably accept that "RF" and light are really just manifestations of the same phenomena (at different frequencies), but I don't think we should assume that, just because we use the term "RF" they are electromagnetic phenomena. We can transmit and receive light and RF by electromagnetic means (antennae), and we can transmit and receive light and RF by non-electromagnetic means (although electrons are certainly involved). The transmission method and the reception method need not be the same.

Certainly, electromagnetic models work well at the lower frequencies and photonic models work well at the higher frequencies, but just because they do, it does not mean we should infer too much about what is going on in space between the transmitter/source and receiver/receptor.

lyner

geezer??Light and Radio waves are electromagnetic phenomena. What else could they be?"RF" refers to frequency and that is not wave-specific - you can get 10MHz ultrasound, for instance.

lightarrowYour earlier long answer to my queries mostly makes sense. There is a phase change at an interface (classical theory) between media but the delay for atomic transitions relates to the Q of the resonance - high Q, slow transition. For conduction electrons / large structure, the Q is very low so the response can be very fast - a fraction of a cycle.Your 10-8 s figure does not have to apply so there is no conflict, I think.

lyner

geezerWhy would you want not to have waves? All observations of the way light and radio travel, point to the wave properties (diffraction, for a start, then the behaviour in guided wave structures). Maxwell relates varying electric and magnetic fields in space is pretty well established and supported by much evidence.To consider that these waves travel through the medium of space is no harder than anything that you may be proposing. If we are having to stretch our imaginations then the less we need to stretch them, the better imho.

What "non-electromagnetic means" do you suggest for transmitting and receiving light and radio? I can't think of any.

Most of us probably accept that "RF" and light are really just manifestations of the same phenomena (at different frequencies), but I don't think we should assume that, just because we use the term "RF" they are electromagnetic phenomena.

It's a kind of joke? I haven't understood it...

Quote

We can transmit and receive light and RF by electromagnetic means (antennae), and we can transmit and receive light and RF by non-electromagnetic means

For example with what? Nuclear interactions? Gravitational interactions?Even if you heat a piece of iron with a flame to become red-hot, it *is* an electromagnetic mean, because you kick the iron's atom with the flame's atom through electromagnetic interactions.

Quote

(although electrons are certainly involved). The transmission method and the reception method need not be the same.

Certainly, electromagnetic models work well at the lower frequencies

You intended "wave models".

Quote

and photonic models work well at the higher frequencies, but just because they do, it does not mean we should infer too much about what is going on in space between the transmitter/source and receiver/receptor.

Infact we don't. Note that I didn't say that light *is* a wave (or a particle) in between source and detector, but that you *talk* about waves or particles. Actually QM description never says anylonger that quantum objects *are* waves or particles, from ≈ 80 years.

geezerWhy would you want not to have waves? All observations of the way light and radio travel, point to the wave properties (diffraction, for a start, then the behaviour in guided wave structures). Maxwell relates varying electric and magnetic fields in space is pretty well established and supported by much evidence.To consider that these waves travel through the medium of space is no harder than anything that you may be proposing. If we are having to stretch our imaginations then the less we need to stretch them, the better imho.

What "non-electromagnetic means" do you suggest for transmitting and receiving light and radio? I can't think of any.

Sophiecentaur,

By "non-electromagnetic" I meant "not by means of antennae". In other words, chemical, atomic interactions etc. Probably not a very good definition, I admit!

While I do appreciate that wave theories and particle theories provide excellent prediction models, I am conflicted that there are two. I am probably more interested in trying to understand the nature of space, even though I'm sure I never will.

Space is the final frontier - wait a minute, didn't somebody already say that?Anyway, space is all around us and even in us, but I don't think we know too much about it IMABHO.

Perhaps Lightarrow, who has lots of knowledge on the subject, can point me to some helpful references?

While I do appreciate that wave theories and particle theories provide excellent prediction models, I am conflicted that there are two. I am probably more interested in trying to understand the nature of space, even though I'm sure I never will.Perhaps Lightarrow, who has lots of knowledge on the subject, can point me to some helpful references?

Geezer, you are not the only one to be conflicted. It's from the 20' of last century that physicists feel conflicted with quantum mechanics . There isn't an answer which is satisfying enough for all people, yet. Maybe you can prefer one specific of the many interpretations of QM. The most followed are written here, for example:http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics

the ortodox one is called Copenhagen Interpretation; the one I prefer at the moment is Relational Interpretation.Choose the one you prefer and enjoy...

The Naked Scientists® and Naked Science® are registered trademarks.
Information presented on this website is the opinion of the individual contributors and does not reflect the general views of the administrators, editors, moderators, sponsors, Cambridge University or the public at large.